Forecasting Significant Wave Height Exceedance Probability Using Regression Models and Cumulative Distribution Functions

Core Concepts

A novel approach for estimating the exceedance probability of significant wave height by leveraging the forecasts of a regression model and the cumulative distribution function.

Abstract

The paper presents a novel approach for estimating the exceedance probability of significant wave height (SWH) time series. The key idea is to leverage the numeric forecasts produced by a regression model and use the cumulative distribution function (CDF) to compute the exceedance probability. The authors first formalize the problem of SWH forecasting as a time series prediction task, where the goal is to predict the future values of the SWH time series. They experiment with several regression models, including random forest regression, LASSO, a heterogeneous regression ensemble, and a deep neural network. To estimate the exceedance probability, the authors propose a method that uses the CDF of the predicted SWH values. Specifically, they assume the predicted values follow a Normal distribution with the mean being the forecast and the standard deviation computed from the training data. The exceedance probability is then calculated as the complement of the CDF evaluated at the predefined threshold. The authors compare the proposed CDF-based approach with two alternative strategies for estimating exceedance probability: binary classification models and ensemble-based direct methods. The experiments are conducted on a real-world SWH dataset collected from a buoy near Halifax, Canada. The results show that the proposed CDF-based method, when coupled with a strong regression model like a deep neural network, outperforms the alternative approaches in terms of the area under the ROC curve (AUC) metric. The authors also analyze the impact of the forecasting horizon and the sensitivity to different probability distributions. Overall, the paper presents a novel and effective approach for estimating the exceedance probability of SWH, which can be valuable for managing maritime operations and renewable energy production.

Stats

The significant wave height (SWH) time series has an hourly granularity and spans from 11-02-2000 15:00:00 to 01-04-2020 11:00:00. The average threshold for exceedance, computed as the 95th percentile of the SWH data, is 3.17 meters.

Quotes

"Forecasting the ocean wave conditions is valuable for multiple operations. The main motivation is related to renewable energy, where forecasts are used to estimate energy production. Moreover, these forecasts are also useful for managing the safety of maritime operations." "We frame the prediction of impending large values of a time series as an exceedance probability forecasting problem. Exceedance probability forecasting denotes the process of estimating the probability that a time series will exceed a predefined threshold in a predefined future period."

Key Insights Distilled From

Exceedance Probability Forecasting via Regression for Significant Wave Height Prediction

by Vitor Cerque... at arxiv.org 04-26-2024

https://arxiv.org/pdf/2206.09821.pdf

Deeper Inquiries

How can the proposed CDF-based method be extended to handle multiple thresholds for exceedance probability estimation, similar to the triple barrier method used in quantitative trading?

The proposed CDF-based method can be extended to handle multiple thresholds for exceedance probability estimation by incorporating a multi-threshold approach. Similar to the triple barrier method used in quantitative trading, where different thresholds are set for buy, sell, or hold signals, the CDF-based method can be adapted to predict the probability of exceeding multiple thresholds. One way to achieve this extension is to define multiple thresholds of interest and compute the exceedance probability for each threshold using the CDF of the predicted values. By calculating the probability of exceeding each threshold, a decision-making framework can be established to determine the appropriate action based on the predicted probabilities. This approach allows for a more nuanced understanding of the likelihood of different levels of exceedance events, enabling better risk management and decision-making.

What are the potential limitations of the analytical approach based on the CDF compared to a Monte Carlo simulation-based approach for estimating exceedance probability?

While the analytical approach based on the CDF offers several advantages, such as computational efficiency and simplicity, there are potential limitations compared to a Monte Carlo simulation-based approach for estimating exceedance probability: Assumption of Distribution: The CDF-based method relies on assuming a specific distribution (e.g., Normal distribution) for the data, which may not always accurately capture the underlying data distribution. In contrast, a Monte Carlo simulation allows for more flexibility in modeling complex and non-standard distributions. Handling Non-linearity: The CDF-based method may struggle to capture non-linear relationships and complex interactions in the data, especially in cases where the data exhibits non-linear patterns or dependencies. Monte Carlo simulations can better handle non-linear relationships and interactions. Risk of Overfitting: The CDF-based method may be prone to overfitting if the assumed distribution does not accurately represent the data. In contrast, Monte Carlo simulations can provide a more robust estimation by generating multiple samples and capturing the variability in the data. Complexity of Implementation: Implementing a Monte Carlo simulation-based approach may require more computational resources and time compared to the analytical CDF-based method, especially for large datasets or complex models.

How can the proposed method be adapted to handle non-stationary time series or time series with complex seasonal patterns, which are common in real-world applications?

To adapt the proposed method to handle non-stationary time series or time series with complex seasonal patterns, several modifications and enhancements can be implemented: Incorporating Seasonal Components: Include seasonal components or features in the predictive model to capture the complex seasonal patterns present in the data. This can involve adding lagged seasonal variables or using seasonal decomposition techniques to extract seasonal trends. Time Series Decomposition: Apply time series decomposition methods, such as seasonal-trend decomposition using LOESS (STL), to separate the time series into trend, seasonal, and residual components. This decomposition can help in modeling and forecasting each component separately. Dynamic Modeling: Implement dynamic modeling techniques that can adapt to changes in the data distribution over time. This can involve using adaptive learning algorithms or recurrent neural networks that can capture temporal dependencies and adjust to non-stationarity. Ensemble Methods: Utilize ensemble methods to combine predictions from multiple models trained on different segments of the time series. This can help in capturing the variability and complexity of non-stationary data. By incorporating these strategies, the proposed method can be enhanced to effectively handle non-stationary time series and complex seasonal patterns commonly encountered in real-world applications.